Enhancement of Blurred and Noisy Images Based on an Original Variant of the Total Variation

Authors:
Khalid Jalalzai;Antonin Chambolle
Affiliations:
Centre de Mathématiques Appliquées (CMAP), École Polytechnique, Palaiseau Cedex, France 91128;Centre de Mathématiques Appliquées (CMAP), École Polytechnique, Palaiseau Cedex, France 91128
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

In this paper, we introduce a new variant of the total variation (TV ). Its purpose is to simplify TV -based restoration when the image is degraded by some kernel which is easily computed in the Fourier domain (blur, Radon transform...). We actually replace the TV term by a mere L 1 norm of some field, for which the optimization is much easier. This approach permits us to use a recent and fast algorithm to enhance, in particular, blurred and noisy images. We also compare our approach with standard total variation based denoising and show that it avoids the famous staircasing effect.